EP2060688A1 - Kit avec trois planches pour la formation des structures polyédriques selon la loi des Cosinus - Google Patents

Kit avec trois planches pour la formation des structures polyédriques selon la loi des Cosinus Download PDF

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Publication number
EP2060688A1
EP2060688A1 EP07398016A EP07398016A EP2060688A1 EP 2060688 A1 EP2060688 A1 EP 2060688A1 EP 07398016 A EP07398016 A EP 07398016A EP 07398016 A EP07398016 A EP 07398016A EP 2060688 A1 EP2060688 A1 EP 2060688A1
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EP
European Patent Office
Prior art keywords
bars
bar
length
kit
holes
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP07398016A
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German (de)
English (en)
Inventor
Luís Nobre Gonçalves
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Universidade Nova de Lisboa
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Universidade Nova de Lisboa
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Publication date
Application filed by Universidade Nova de Lisboa filed Critical Universidade Nova de Lisboa
Priority to EP07398016A priority Critical patent/EP2060688A1/fr
Publication of EP2060688A1 publication Critical patent/EP2060688A1/fr
Withdrawn legal-status Critical Current

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    • E—FIXED CONSTRUCTIONS
    • E04—BUILDING
    • E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
    • E04B1/00—Constructions in general; Structures which are not restricted either to walls, e.g. partitions, or floors or ceilings or roofs
    • E04B1/38—Connections for building structures in general
    • E04B1/58—Connections for building structures in general of bar-shaped building elements

Definitions

  • the main field of this invention is mechanical engineering where a kit of bars constitutes engineering elements for construction of generic structures.
  • the structures have elongated members which are designed for the purpose of being joined to similar members in various relative positions.
  • the object of this invention is an engineering structure construction system that simultaneously maximizes structure diversity and minimizes the system complexity.
  • W09921669 by Massimo Ferrante and Mario Amato as it deals with METAL OR NON METAL SECTION BARS WITH "L”, “U”, “Z” SHAPED CROSS SECTIONS.
  • the kind of bars mentioned in document W09921669 differs from the present three bars kit in the absence of a geometric requirement for the thickness of the material. This means that the diversity of polyhedric structures which can be built with one of "L", “U” or “Z” shaped cross section bars is small when compared with the diversity of polyhedric structures which can be built with one of the three bars from the three bars kit.
  • Patent PT103301 is entirely general in respect to the types of polyhedric structures that can be built with it. This generality results from the fact that angles and lengths are selected from continuous ranges. Unfortunately, this generality comes at the cost of a need for iterative processes to reach the final form of the structures. In the absence of preformed gauges or shapes, the angles and the lengths start out wrong. This just cannot happen with the present three bars kit because angles and lengths are selected from a finite set of discrete values. The three bars kit gives total surety about matching dimensions together with good generality.
  • the present invention is a three bars kit constituted by three kinds of bars, where the bar of kind (1) has uniform square convex hull section along its length, and both the other two bars, the bars of kinds (2) and (3), have equal and uniform regular hexagonal convex hull sections along their lengths.
  • the three bars provide the means to construct generic complex engineering structures that can be thought of as assemblies of simple sub-structures like: triple connections as shown in Figures 4 , 5 , 6 and 7 ; sheaves of bars mutually connected in parallel as shown in Figures 8 , 9 and 10 ; polygons whose edges have integer length as shown in Figure 11 ; quadruple connections as shown in Figures 16 and 17 ; etc.
  • Another example is that one may build one triangle with integer sides of two different unit lengths (whose ratio is irrational) and still have a rational cosine (of course, this is not exactly true but very good approximations may be found). This is the reason why bars of kind (3) are "somewhat" compatible with the other kinds in respect to the assembly of triangles. It is always possible to make triangles with sides of any length (as far as no length is greater than the sum of the other two) but it is not always possible to make triangles with given length ratios and given angles.
  • the basic elements of the present invention can produce, among other sub-structures, the ones named “triple connections” and “quadruple connections”. These are described below.
  • a triple connection is a connection of three bars where no two bars are parallel and where each pair of bars is connected at a single point (there are three connection points in a triple connection).
  • Triple connections are very significant in this invention because they implement a simple and mechanically robust way to move beyond planar structures and into the third dimension.
  • the three bars kit provides four kinds of triple connections (see Figures 4 , 5 , 6 and 7 ). Any pair of bars in a triple connection defines a plan and the third bar of that same triple connection is both out of that plan and fixed at two points.
  • a quadruple connection is a group of four bars mutually connected at four points, two of the bars being of the same kind and the other two bars being of some other kind and parallel. There is a very large number of different quadruple connections, but one may be set apart.
  • This special quadruple connection is made of two parallel bars of kind (1) and two bars of kind (2). When in the special configuration, the absolute value of the cosine of the angle between two bars of different kind is one half (see Figure 16 ). No other quadruple connection with rational cosines for the angles between a parallel bar and an oblique bar was found. The importance of rational cosines is described below. Also worth mentioning is another quadruple connection made with two bars of kind (3) and two parallel bars both of kind (2) or (3). It is possible to assemble this connection so that the angles between any of the two oblique bars and any of the two parallel bars are exactly 45 degrees (see Figure 17 ).
  • Structures containing triangles whose edges have integer length may be designed considering the law of cosines.
  • Triangles are the only kind of planar polygons whose internal angles are inherently fixed and, therefore, triangles are required for rigid structures.
  • connections between bars are supposed to be made through the holes with standard industrial connectors like rivets, nuts and bolts or the like. It should also be noted that the law of cosines is still valid when A, B and/or D are not integer and/or C is not rational.
  • Each bar of the kit represents a kind of bar which is identified with the numbers (1), (2) or (3).
  • the bar of kind (1) has uniform square convex hull section along its length.
  • the bars of kind (2) and (3) have equal and uniform regular hexagonal convex hull sections along their lengths.
  • the three bars (of kind (1), (2) and (3)) have holes directed perpendicularly to the sides of the convex hulls, directed perpendicularly to the length of the bars and crossing exactly through the centre of the convex hulls, all holes on each bar having the same diameter.
  • the bar of kind (1) has holes distributed periodically along its length, with a single wave vector of norm 2xL, one hole every L /2 length and changing sides only once every L length.
  • the bar of kind (2) also has holes on two pairs of opposite sides distributed periodically along the length of the bar, one hole every L /2 length and changing to the other of the two pairs of opposite sides only once every L length.
  • the bar of kind (2) additionally has holes on one pair of opposite sides distributed periodically along the length of the bar, one hole every G /2 length.
  • the bar of kind (2) can also have one reference hole on the G /2 wave vector side(s) such that its geometric centre is exactly at mid-distance between two adjacent pairs of holes on the other side(s).
  • the bar of kind (3) has holes on all of its sides, distributed periodically along its length, with a single wave vector, with one hole every J /3 or J /6 length, holes separated by a distance J being on different sides and existing at least one chosen side where holes separated by a distance 2x J /3 are on that same chosen side.
  • Any bar (of kind (1), (2) or (3)) cooperates with any other bar (of kind (1), (2) or (3)) by means of some hole, configuring a rotation axle without angular limits.
  • Any bar (of kind (1), (2) or (3)) can also cooperate with any other bar (of kind (1), (2) or (3)) with wave vectors and sides scaled by a factor 1/4, 1/3, 1, 3, or 4, by means of two or more holes, configuring a reinforced or extended composite bar, with the exception of bars (1) and (3) which cannot mutually cooperate by means of more than one hole.
  • the height H of the bars of kind (2) or (3) must be ( ⁇ 3-1)xL, where L is the length of the side of bars of kind (1), for both triple connections of Figures 5 and 6 to be possible.
  • All bars must have holes perpendicular to their convex hull surface so that standard industrial connectors may be used. Even distribution of stresses is ensured when the holes cross the centre of the bar's section.
  • Bars (1) and (2) have holes distributed periodically along their lengths, with a wave vector of norm 2x L , one hole every L /2 length and changing side only once every L length, because of two reasons: (i) a reduced unit length ( L /2) increases the angle coverage for the same maximum bar length and (ii) only holes on different sides and separated by a distance L allow the triple connections of Figures 4 , 5 and 6 .
  • Bars (2) and (3) are easier to use together if they share at least one wave vector on at least one side.
  • Bars of kind (3) can be assembled in a triple connection (as in Figure 7 ) only if they have holes on different sides separated by a distance J .
  • Angle coverage is, again, increased if one uses shorter unit lengths.
  • a reasonable unit length is J /3 because it represents not too many holes and implies drilling patterns recognisably different from those of bars (2).
  • the structures may contain instances of just one kind of bar, instances of any pair of kinds of bar or instances of all three kinds of bar.
  • each kind of bar may exist in several different scales.
  • a given structure may contain both bars of side length equal to L and bars of side length equal to K x L where K may be 1/4, 1/3, 3, 4 or products of integer powers of these values.
  • K may be 1/4, 1/3, 3, 4 or products of integer powers of these values.
  • reference holes of bars of kind (2) should be clearly marked.
  • the definition of "reference hole” is given in claim 7 but one should note that only bars of kind (2) have reference holes and that each bar may have at most one reference hole.
  • the bars may be manufactured by means of different processes and using many different materials but, due to the fact that there are only three kinds of bars, we believe that the process of injection can be optimized efficiently for many different instances of bars. It should be noted, however, that different instances may be manufactured by different processes. Furthermore, given that most standard connectors will induce compression stresses along the holes, it is foreseen as adequate both the avoidance of intersections between holes and the full extension of their sleeves from side to side of the convex hulls.

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  • Engineering & Computer Science (AREA)
  • Architecture (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Civil Engineering (AREA)
  • Structural Engineering (AREA)
  • Toys (AREA)
EP07398016A 2007-11-13 2007-11-13 Kit avec trois planches pour la formation des structures polyédriques selon la loi des Cosinus Withdrawn EP2060688A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
EP07398016A EP2060688A1 (fr) 2007-11-13 2007-11-13 Kit avec trois planches pour la formation des structures polyédriques selon la loi des Cosinus

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
EP07398016A EP2060688A1 (fr) 2007-11-13 2007-11-13 Kit avec trois planches pour la formation des structures polyédriques selon la loi des Cosinus

Publications (1)

Publication Number Publication Date
EP2060688A1 true EP2060688A1 (fr) 2009-05-20

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EP07398016A Withdrawn EP2060688A1 (fr) 2007-11-13 2007-11-13 Kit avec trois planches pour la formation des structures polyédriques selon la loi des Cosinus

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Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1999021669A1 (fr) 1997-10-24 1999-05-06 Aluterm S.R.L. Barres profilees metalliques ou non metalliques avec sections transversales en l, en u et en z, pour la realisation de cadres de support structurels pour panneaux de placoplatre et similaires, et procede de fabrication de ces barres
WO2000045083A1 (fr) 1999-01-26 2000-08-03 Salvatore Mocciaro Système de construction universel
WO2004024277A2 (fr) 2002-09-13 2004-03-25 Timothy John Warner Construction kit
EP1640524A2 (fr) * 2004-09-23 2006-03-29 Sikla GmbH & Co. KG Kit de construction pour réaliser une structure de support, en particulier pour tubes
PT103301A (pt) 2005-06-30 2006-12-29 Univ Nova De Lisboa Peças para construir estruturas poliédricas

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO1999021669A1 (fr) 1997-10-24 1999-05-06 Aluterm S.R.L. Barres profilees metalliques ou non metalliques avec sections transversales en l, en u et en z, pour la realisation de cadres de support structurels pour panneaux de placoplatre et similaires, et procede de fabrication de ces barres
WO2000045083A1 (fr) 1999-01-26 2000-08-03 Salvatore Mocciaro Système de construction universel
WO2004024277A2 (fr) 2002-09-13 2004-03-25 Timothy John Warner Construction kit
EP1640524A2 (fr) * 2004-09-23 2006-03-29 Sikla GmbH & Co. KG Kit de construction pour réaliser une structure de support, en particulier pour tubes
PT103301A (pt) 2005-06-30 2006-12-29 Univ Nova De Lisboa Peças para construir estruturas poliédricas

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